Hey Ripper, I used to think that too, but guess what? Evidently, THAT'S A GARDENING MYTH! And here's a link to an organic gardening video made by a guy up in Canada who put that myth through the test.
(The part about chlorine begins about three and a half minutes in.)
There may be lots of reasons to use R.O. or distilled water, but apparently chlorine isn't one of them. Poor water quality, (some folks live where their water has a ppm of 1750 out of the tap!) definitely justifies filtered or distilled water, but if you are using distilled out of the belief that chlorine will "kill the herd", you may be working too hard and spending too much money at it.
I know....it floored me too! But IT'S A GARDENING MYTH!!!